An accelerated life test (ALT) is commonly used in reliability studies of high quality products. A step-stress experiment is one such ALT that is often used in practice. In this paper, we develop exact inference based on likelihood-ratio test for a simple step-stress model with exponential lifetimes under Type-II censoring. We consider both unrestricted and order-restricted maximum likelihood estimators (MLEs) for this purpose. We also derive the exact power function of this test, which we then use for designing an optimal step-stress testing experiment. By using a similar approach, we extend these results to other forms of censoring. Monte Carlo simulations are then carried out to evaluate the performance of the inferential methods developed here. Finally, an illustrative example is presented for demonstrating all the inferential results.

中文翻译：

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具有删失指数数据的简单阶梯式累积累积模型的精确似然比检验

加速寿命测试（ALT）通常用于高质量产品的可靠性研究中。逐步压力实验就是这样一种ALT，经常在实践中使用。在本文中，我们基于II型删失下具有指数寿命的简单阶跃应力模型，基于似然比检验开发了精确的推论。为此，我们同时考虑了无限制和有顺序限制的最大似然估计器（MLE）。我们还导出了该测试的精确功效函数，然后将其用于设计最佳阶跃应力测试实验。通过使用类似的方法，我们将这些结果扩展到其他形式的审查。然后进行蒙特卡洛模拟，以评估此处开发的推理方法的性能。最后，给出了一个说明性示例，以演示所有推论结果。